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551
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 4
J. M. CALIXTO | T. H. SOUZA | E. V. MAIA
are below the appropriate safety range (smaller than 0.85) with
2% in the extremely dangerous zone (smaller than 0.5). This fact
shown in Table 3. A score value smaller than 0,5 is worse in terms
of safety than one greater than 2. On the other hand, a score value
equal 2, corresponded to the low safety zone is attributed to an
extremely conservative ratio for being not economical. The total
demerit point score of each design code equation is calculated by
summing the products of the percentage of
M test
/
M pred
obtained
in each range times the demerit value attributed to that range. The
largest the total demerit point score is the worst is the performance
of the design equation.
3 Results and analysis
3.1 Columns made with concrete of f
c
≤ 55 MPa
The results of the
M test
/
M pred
ratio for columns made with con-
crete of
f
c
≤ 55 MPa
are presented in the Table 4. They were
obtained from the comparison with test results of 51 columns. The
analysis of these results reveals that NBR 6118 [1] approximate
stiffness criterion is more conservative than the approximate cur-
vature method: average and median values are larger than the
unity. In terms of accuracy, the approximate stiffness procedure is
also more precise, since the coefficient of variation is 2% smaller.
With respect to safety, the demerit scale (shown in the part B of
Table 4) reveals that the results obtained with the approximate cur-
vature method are of concern: 22% of the
M test
/
M pred
values
Table 2 – Column database (f > 55 MPa)
c
Research team
Number
of tested
columns
b
(cm)
h
(cm)
l
e
(cm)
l
f
c
(MPa)
r
l
(%)
LEE and SON [7]
14
12
12
138 - 210
40 - 61
70,4 to 93,2 1,98 to 5,51
LIMA JÚNIOR [9]
3
15
15
195
45
66,4
2,18
LLOYD and RANGAN [14]
18
30
10
168
58
58 to 97,2 1,51 to 2,26
CLEASON and GYLLTOFT [13] 6 12 - 20 12 - 20 260 - 420 55 - 75 86 to 93 2,1 to 3,2
GALANO and VIGNOLI [12] 24
10
10
212
73,4 75,2 to 113,3 2,01 to 4,52
Table 3 – Demerit Point Classification
of Collins [4]
Classification
M /M
test
pred
Score
Extremely dangerous
< 0.50
10
Dangerous
0.50 |---- 0.65
5
Low Safety
0.65 |---- 0.85
2
Appropriate Safety
0.85 |---- 1.30
0
Conservative
1.30 |---- 2.00
1
Extremely Conservative
≥
2.00
2
Table 4 – Columns made with
concrete of f
≤
55MPa
c
Parameters
M /M
test
pred
Approximate
Curvature
Method
Approximate
Stiffness
Procedure
Average (m)
Median (m )
d
Standard
deviation (SD)
Coefficient of
variation (CV)
0,962
0,978
0,178
18,55 %
1,051
1,073
0,173
16,43 %
Part A – Statistical Analysis
Part B – Demerit Point Classification
M /M
test
pred
Approximate
Curvature
Method
Approximate
Stiffness
Procedure
0.65|--0.85
13,7
7,8
0.85|--1.30
76,5
86,3
1.30|--2.00
2
2
≥
2
.
00
0
0
Total Demerit
Point Score
79**
37
< 0.50
2*
0
0.50|--0.65
5,9
3,9
* – Percentage values of M /M results
test
pred
**79 = (2 x 10) + (5,9 x 5) + (13,7 x 2) + (76,5 x 0) + (2 x 1) + (0 x 2)